SOLUTION: 1)A farmer wishes to grow a 100 m^2 rectangular vegetable garden.Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall
Question 10269: 1)A farmer wishes to grow a 100 m^2 rectangular vegetable garden.Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his houseact as the fourth side-fence.Find the dimensions of his garden.
[Hint:If the length of one side is x metres, the other side will be (30-2x)m.Therefore,x(30-2x)=100] Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website! Your set up is right. Just solve the equation, which is a quadratic equation. These types of equations nearly almost always factor. You are letting x = the length of each of the two equal sides, where the 30-x represents the side parallel to the house.
x(30-2x) = 100
Set the equation equal to zero, preferably with the term positive. To do this take everything to the right side, by adding to each side of the equation.
From this, you can factor out the common factor of 2.
Now factor the trinomial:
There are two solutions:
x=5, x=10
If x=5 m, the other side is 30-2x = 20 m.
If x = 10 m, the other side is 30-2x = 10 m.
Both solutions work in that the perimeter is 30 m, and the area is 100 m^2.
